ACTA UNIVERSITATIS AGRICULTURAE ET SILVICULTURAE MENDELIANAE BRUNENSIS

Volume 64 146 Number 4, 2016 http://dx.doi.org/10.11118/actaun201664041303

WEATHER RISK MANAGEMENT IN AGRICULTURE

Martina Bobriková1

1 Department of Finance, Faculty of Economics, Technical University of Košice, B. Nemcovej 32, 040 01 Košice, Slovak Republic.

Abstract

BOBRIKOVÁ MARTINA. 2016. Weather Risk Management in Agriculture. Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, 64(4): 1303–1309.

The paper focuses on valuation of a weather with payoffs depending on temperature. We use historical data from the weather station in the Slovak town Košice to obtain unique prices of contracts in an incomplete market. Numerical examples of prices of some contracts are presented, using the Burn analysis. We provide an example of how a weather contract can be designed to the financial risk of a suboptimal temperature condition. The comparative comparison of the selected option hedging strategies has shown the best results for the producers in agricultural industries who hedges against an unfavourable weather conditions. The results of analysis proved that by buying or , the farmer establishes the highest payoff in the case of temperature decrease or increase. The Long Strategy is the most expensive but is available to the farmer who hedges against a high in temperature movement. We conclude with the findings that weather derivatives could be useful tools to diminish the financial losses for agricultural industries highly dependent for temperature.

Keywords: weather derivative, option contract, temperature, Burn analysis, hedging

INTRODUCTION Ender and Zhang, 2015) analyze weather derivatives Weather often has a significant impact on as the potentially effective risk management tool for agricultural production. Climate change has agricultural industries. increased the frequency and intensity of catastrophic Like stated Alexandridis and Zapranis (2013) weather events that can caused serious financial weather derivatives can be used by corporations damages to the farmers (see, e.g., Černý et al., 2013; or individuals as part of risk management strategy Fukalová et al., 2014; Velecká et al., 2014). Actually, to reduce, i.e. hedge, risk associated with adverse it is to be expected that weather fluctuations will or unexpected weather conditions. They are increase in the future due to climate change (Pérez contracts with the payoff depending on the González and Yun, 2012). temperature, rainfall, snowfall, humidity, sunshine Weather and its changes have driven a demand or wind. Since, the most common underlying for weather risk management. Traditional insurance variable is temperature, temperature derivatives can be used to avoid high losses coming from will be considered in this paper. Weather market catastrophic events but it does not provide an is incomplete in the sense that the underlying adequate solution to mitigate financial losses which weather assets are not tradable. Therefore the price are caused by suboptimal weather conditions (Cyr of a weather derivative is usually based on various et al., 2010). Weather derivatives display advantages underlying weather indices. In the majority of over traditional insurances. The management of papers focused on weather derivatives, authors weather risk with derivatives is regular theme of deal with temperature indices Heating Degree Days scientific papers. For example studies (Chenet al., (HDD) index (for the fall and winter months) and 2011; Musshoffet al.; 2011; Spicka and Hnilica, 2013; Cooling Degree Days (CDD) index (the spring and

1303 1304 Ing. Martina Bobriková, Ph.D.

summer months). There are for example works We also design hedging strategies, which can reduce (Considine, 2000; Taušer and Čajka, 2014). Jones economic impacts of temperature. (2011) examines the structure of HDD and CDD Pricing models for weather derivatives exist at contracts along with agricultural hedging uses of many levels of sophistication (see, e.g., Benth and weather derivatives. Benth, 2011; Benth and Benth, 2012; Schiller et al., Weather derivatives are usually structured as 2012; Zapranis and Alexandridis, 2009; Zapranis futures, swaps and option based on different and Alexandridis, 2011). The model shown here is underlying weather indices (see, e.g., Dischel, 2002). not necessarily what the market makers use. This In this work we will only study call/put weather said, a simple model can give a rough idea of what options. The buyer of a call option will receive a an option should cost. Our findings help to raise payoff if the underlying weather index value is the ability of them to understand the application of greater than the predetermined strike level at the weather derivatives in order to reduce the financial maturity day. The buyer of a put option will receive risk of suboptimal temperature events. Weather a payoff if the predetermined strike level is greater derivatives can be very useful to risk managers who than the underlying weather index value at the understand options and the risk profile associated maturity day. The buyer of a call/put option pays the with buying and selling weather options relative to seller a premium at the beginning of the contract. their business. When investors start to look at the Alaton et al. (2002) stated that a weather option can be weather for hedging purposes, formulated by specifying the following parameters: increased liquidity as well as new products will contract type, contract period, weather station probably follow. from which the temperature data are obtained, underlying weather index, strike level. MATERIALS AND METHODS Weather options are either negotiated between two parties in the Over-The-Counter (OTC) market There is not a market for weather derivatives or traded on organized exchanges. The first exchange in Slovakia. This is attributed to the fact that it where standard weather derivatives could be traded is unclear whether and to what extent weather was the Chicago Mercantile Exchange (CME). derivatives are a useful instrument of risk Although the use of weather derivatives is now management. Since the most common underlying widespread and increasing, the European market variable is temperature, only the temperature based has not developed as quickly as the US market. The derivatives will be considered in this paper. A simple key fact is that their understanding by potential pricing formula for an option contract depending issuers and investors (primarily agricultural and on temperature index HDD will be suggested. energy industries) has been relatively poor. Agricultural application of weather derivatives to The main aim of this paper is to price and design risk management will be indicated. a weather derivative and to present the hedging The data were collected for the studied area Košice. strategies of a suboptimal weather. Based on the data Our methodology can be applied to different cities. set, we price the call/put options with the payoff The time period consists of 30 years (from 1984 to depending on temperature index HDD, using the 2013) with 10,958 observations. The data consists of Burn analysis. Basic source of data for the option daily minimum and maximum temperatures from pricing were daily average minimum and maximum the weather station in the mentioned area. Historical temperatures from the weather station in Košice. temperature observations were obtained from the National climatic data centre. In Fig. 1 is shown the daily average temperature in the studied area.

30

20 ° C 10

0

-10 emperature in t emperature -20

-30

1: Graph of the daily average temperature development in Košice from 1984 to 2013. (Source: The author’s processing based on historical temperatures from the National climatic data centre.) Weather Risk Management in Agriculture 1305

We use the burn analysis based on historical data The strike prices X calculated according to the from the studied area to compute the price of the papers (Garcia and Sturzenegger, 2001; Platen and option with payoff depending on temperature. The West, 2004; Roustant et al., 2003) have the following price of the option depends on the temperature forms: index and the . Based on commonly used temperature index A : X = annual average HDD; HDD (heating degree-days index) presented by Zapranis and Alexandridis (2009), Benth and Benth (2011) and many others the options are priced. The daily value of the HDD index is:

daily HDD (t) = max (18 - T (t), 0),

where T(t) is the daily average temperature. The daily average temperature is calculated by averaging each day’s maximum and minimum temperature from midnight-to-midnight. To illustrate the RESULTS AND DISCUSSION concept of HDD, suppose that on a given winter day In pricing we consider following parameters: the high temperature was 11 degrees and the low • the risk-free interest rate is AAA-rated Slovakia temperature was 1 degree. This weather results in a government bond yield for 30 years maturity daily average temperature of 6 degrees with 12 HDD relating to the historical data, for this day. The lower is the temperature, the higher • the time of HDD option contract conclusion is 31st is the daily HDD. Weather options are written on of december 2013 and the contract is for annual the cumulative HDD over a specified period. The temperature events, annual payoff is calculated as: • 20% relation to the risk. anual payoff = annual average HDD × tick level. The partial results used in our analysis are in Tabs. I, II. All results can be provided upon request. The owner of a call option obtains the payoff if the HDD index value is higher than the strike price. Assuming the put option owner the payoff is paid if the strike price is higher than the HDD index value. Let us denote the annual average payoff µ, the standard deviation calculated from the annual payoffs σ, the risk-free interest rate r, the maturity date T, the relation to the risk α. The long and short option price is:

long = e-rT (μ + α.σ), short = e-rT (μ − α.σ).

I: Call option pricing Annual average Price of Long Call Price of Short Call Strike price in EUR Standard deviation payoff option in EUR option in EUR 3225.53 6.29 4.54 7.03 5.26 3331.70 5.10 4.86 5.93 4.03 3437.88 2.94 4.57 3.76 1.98 Source: The author’s own calculations

II: Put option pricing Annual average Price of Long Put Price of Short Put Strike price in EUR Standard deviation payoff option in EUR option in EUR 3225.53 2.83 4.07 3.56 1.97 3331.70 4.02 4.38 4.78 3.07 3437.88 6.18 4.13 6.84 5.23 Source: The author’s own calculations 1306 Ing. Martina Bobriková, Ph.D.

Weather risk for producers in agricultural For an option buyer, the premium represents the business refers to the uncertainty about the maximum cost or amount that can be lost, since the expected weather conditions. If a farmer wanted to option buyer is limited only to the initial investment. have protection from an extremely cold winter he The comparison of incomes of WO1, WO2 and could buy HDD call options or HDD put options, WO3 at various development of HDD index value at for an extremely hot winter. For example, if a wheat the maturity time of options is shown in Fig. 2. It can farmer wanted to use options to hedge his cold be seen, but also be calculated exactly using income weather risk, he could buy HDD call options for a function presented above, that: some city at a some strike. The buyer of a weather • the weather option 3 (with a strike price 3437.88 option has theoretically unlimited profit potential calculated using fomula C), if the HDD index on the upside, while only risking the premium value at the maturity date of options is lower than paid for the option on the downside. This limited 3228.80; downside risk is transferred to the writer of the • the weather option 1 (with a strike price 3225.53 option, who accepts potentially unlimited downside calculated using fomula (B)), if the HDD index risk in return for receiving the option premium value at the maturity date of options is higher than at the time of the sale. The HDD options are 3232.56. European style, which means that they cannot be The lower the strike price, the higher the income exercised before their respective maturity dates. The from the call option. The income is unlimited, the following hedging strategies based on HDD index loss is limited by the option premium. The weather are examples of how to manage weather risk using option 1 ensures the highest profit. The cost of this option contracts. benefit is the highest option premium. This hedging Let construct a call option on HDD index with variant is available to the farmer with a higher various strike prices. We assume that the call option degree of risk aversion. Low-risk-aversion farmer on the HDD index will buy a farmer whose profits will prefer the weather option 3. The weather option are affected by low temperatures. 2 is the most suitable hedging strategy for the farmer The future payoff for every scenario is given in the with a neutral risk aversion. It should be noted that, Tab. III. Two variants of the scenario can occur at the only the weather option with the strike price 3331.70 maturity of an option. If the HDD index value at the is used for further analysis. maturity date T is below the strike price X, then the farmer will lose the option premium CB which is the cost of risk management benefit. If the HDD index value at the maturity is above the strike price, then the farmer will obtain the payoff of (HDD − X − CB).

III: Payoff from the buying call option HDD index value Payoff scenario

HDD

HDD≥X HDD−X−CB Source: The author’s processing

On 31 December 2013 we will buy the call option 2: Graph illustrated payoff from the weather options 1, 2 and 3 on HDD index with the strike price X = 3225.53. The proposed for Košice. Source: The author’s processing income function for weather option 1 (WO1) is:

-.703 if HDD < 3225.,53 The Long Put strategy is a simple bearish strategy. PH ()DD = 1 { HDD-.3232 56 if HDD ≥ 3225..53 By buying put option the buyer hedge against a temperature increase. The following table lists the The income function for weather option 2 (WO2) payoff from buying put option. with the strike price X = 3331.70 has the following form: IV: Payoff from the buying put option -.593 if HDD < 3331.,70 HDD index value PH2 ()DD = Payoff { HDD-.3337 63 if HDD ≥ 3331..70 scenario

HDD

Assume the put option on HDD index with the Producers in agricultural industries should learn strike price X = 3331.70. The income function of how to evaluate and compare option and option weather option 4 (WO4) is expressed by the formula: strategies. The Fig. 3 compares weather options 2, 4 and 5 and illustrates the payoff at the maturity -HDD +3326.92 if HDD<3331.70, P (HDD) = date under potential HDD index values. Each of the 4 { -4.78 if HDD ≥ 3331.70. strategies has their own strengths and weaknesses. Results of the analysis of weather options 4: • if the HDD index value at the maturity date of options is lower than 3326.92, then the hedger is profitable; • otherwise, he suffers a financial loss 4.78. Options may be combined, by means of which new forms and attractive investment opportunities are created. Option strategies can offer opportunities and advantages to protection or investment from changes in values of various underlying assets and can be also used in the creation of modern structured products. More detailed information about structured products’ creation can be found, e.g., in works (Šoltés, 2010; Šoltés, 2011; Harčariková, 2015; Harčariková and Bánociová, 2015; Šoltés and 3: Graph illustrated the payoff from the weather options 2, 4 and 5 Harčariková, 2015; Šoltés and Pinka, 2015). Much proposed for Košice. Source: The author’s processing of the trading is concentrated in several popular strategies such as and put, bull and , and straddle. We want to It can be seen, but also be calculated exactly using demonstrate that option strategies can also be a functions of WO2, WO4 and WO 5 that: weather risk management tool. • the buying put option ensures the highest payoff if Long Straddle strategy is a neutral strategy that is the HDD index value at the maturity date is lower formed by buying a put option with a strike price than 3326.92, but it does not enable to participate X and option premium pB and at the same by in the HDD index value increase; buying a call option with a same strike price X and • the buying call option ensures the highest payoff if option premium cB. The payoff for every scenario is the HDD index value at the maturity date is higher indicated in the Tab. V. than 3337.63, but it does not enable to participate on the HDD index value decrease; V: Table Payoff from Long Straddle strategy • the farmer is unprofitable if the HDD index value at the maturity date is between 3326.93 and HDD index value Payoff 3337.63. scenario • the Long Straddle strategy enable to participate −HDD+X−p −c HDD

CONCLUSION It is a common knowledge that weather represents the major source of uncertainty in agriculture businesses. This work contributes to the literature by dealing with weather risk management using weather derivatives with the aim to enhance their understanding. Weather derivatives are increasing in popularity. Yet, there is much more historical data available for the agriculture markets than for other markets. As a result, the use of weather derivatives to hedge agricultural commodities and livestock is increasing. Weather option contracts could be easily used to hedge much of the risk in agricultural commodity volume and in turn lead to increased revenues for farmers and others in agricultural related businesses. This paper focused on risk of unfavourable temperature movements and its negative effects on agricultural production from the economical point of view. We present options with the payoff depending on temperature index HDD. Companies in the agriculture industry, with revenues adversely affected by extremely cold or hot winters, can buy weather contracts and hedge lower revenues during extreme weather conditions. For example, let us suppose the farmer expects the temperature is going to rise in the future. This would be a good time to hedge against a temperature increase in the future using relevant option hedging strategy. With the options, a farmer is protected against an unfavourable temperature change. The data for our analyses has been collected from the 30 years long observations of daily minimum and maximum temperatures from the weather station in Košice, Slovakia. Based on the analysis of these historical data, we price the call/put options using the Burn analysis. Strategy using call option, strategy using put option and Long Straddle strategy for hedging of risks connected with temperature are created. Its economic analysis is performed as well. These hedging strategies are studied in the future scenarios. To conclude, these strategies are effective for the hedging of unfavourable temperature change. In case of extremely cold winter farmer could buy HDD call options, viceversa, for extremely hot winter he could buy HDD put options. Long Straddle strategy is suitable for cold winter and at the same time hot winter. These hedging strategies illustrate the diversity of ways in which agricultural options can be used. The key to using options successfully is the ability of producer to match an appropriate strategy to a particular objective at a given time. The flexibility of strike price selection allows producers to adjust their market risk exposure to any level with which they are comfortable. The strategies we looked at in this paper are fairly common ones, but by no means, there are many other strategies which have to be considered in the agricultural risk management. This article examines the weather derivatives market and some of its benefits for agricultural risk management. Performed analysis should help to understand the pricing and design of the weather derivatives. In particular, this article is meant to serve as an overview of weather derivatives for those who may not be otherwise exposed to this type of market. Further studies are needed to find an option pricing model for weather derivatives with payouts depending on temperature in an incomplete market.

REFERENCES CONSIDINE, G. 2000. Introduction to Weather ALATON, P., DJEHICHE, B. and STILLBERGER, Derivatives. Weather Derivatives Group, Aquila D. 2002. On modelling and pricing weather Energy. derivatives. Applied mathematical finance, 9(1): 1 – 20. CYR, D., KUSY, M. and SHAW, A.B. 2010. Climate ALEXANDRIDIS, A. K. and ZAPRANIS, A. D. 2013. change and the potential use of weather derivatives Weather derivatives. New York: Springer. to hedge vineyard harvest rainfall risk in the BENTH, F. E. and BENTH, J. S. 2011. Weather Niagara region. Journal of Wine Research, 21(2 – 3): Derivatives and Stochastic Modelling 207 – 227. of Temperature. International Journal of ČERNÝ, I., VEVERKOVÁ, A., KOVÁR, M. et al. Stochastic Analysis, 2011: Article ID 576791. 2013. The variability of sunflower (Helianthus doi:10.1155/2011/576791. annuus L.) yield and quality influenced by BENTH, J. Š. and BENTH, F. E. 2012. A critical wheater conditions. Acta Universitatis Agriculturae et view on temperature modelling for application Silviculturae Mendelianae Brunensis, 61(3): 595 – 600. in weather derivatives markets. Energy Economics, DISCHEL, R. S. 2002. Climate Risk and the Weather 34(2): 592 – 602. Market: Financial Risk Management With Weather CHEN, C., LEI, C., DENG, A. et al. 2011. Will higher Hedges. London: Risk Publications. minimum temperatures increase corn production ENDER, M. and ZHANG, R. 2015. Efficiency of in Northeast China? An analysis of historical data weather derivatives for Chinese agriculture over 1965 – 2008. Agricultural and Forest Meteorology, industry. China Agricultural Economic Review, 7(1): 151(12): 1580 – 1588. 102 – 121. FUKALOVÁ, P., STŘEDOVÁ, H. and VEJTASOVÁ, K. 2014. Development and prediction of selected Weather Risk Management in Agriculture 1309

temperature and precipitation characteristics in SPICKA, J. and HNILICA, J. 2013. A methodical Southern Moravia. Acta Universitatis Agriculturae et approach to design and valuation of weather Silviculturae Mendelianae Brunensis, 62(1): 91 – 98. derivatives in agriculture. Advances in Meteorology, GARCIA, A. F. and STURZENEGGER, F. 2001. 2013: Article ID 146036. Doi: 10.1155/2013/146036. Hedging corporate revenues with weather derivatives: ŠOLTÉS, M. 2010. Relationship of speed certificates A case study. [Online]. Available at: http://www. and inverse vertical ratio call back spread option hec.unil.ch/cms_mbf/master_thesis/0004.pdf. strategy. E+M Economics and Management, 13(2): [Accessed 2015, August 26]. 119 – 124. HARČARIKOVÁ, M. 2015. Proposal of new ŠOLTÉS, M. and PINKA, L. 2015. Innovation in outperformance certificates in agricultural Alternative Forms of Investments. Polish Journal of market. Agricultural Economics (Czech Republic), 61(9): Management Studies, 11(1): 168 – 178. 400 – 409. ŠOLTÉS,V. 2011. The Application of the Long and HARČARIKOVÁ, M. and BÁNOCIOVÁ, A. 2015. Short Combo Option Strategies in the Building Analysis of using options to the express certificates of Structured Products. In: Liberec Economic Forum formation. Economic Research‑Ekonomska Istraživanja, 2011: proceedings of the 10th international conference. 28(1): 354 – 366. Technical University of Liberec, 19 – 20 September JONES, T. L. 2011. Agricultural applications of 2011. Liberec: Technical University of Liberec, weather derivatives. International Business & 481 – 487. Economics Research Journal, 6(6): 53 – 60. ŠOLTÉS, V. and HARČARIKOVÁ, M. 2015. Analysis MUSSHOFF, O., ODENING, M., and XU, W. 2011. of Using Barrier Options to the Formation of New Management of climate risks in agriculture–will Structured Products. Mediterranean Journal of Social weather derivatives permeate? Applied Economics, Sciences, 6(2): 303 – 311. 43(9): 1067 – 1077. TAUŠER, J. and ČAJKA, R. 2014. Weather derivatives PÉREZ – GONZÁLEZ, F. and YUN, H. 2013. Risk and hedging the weather risks. Agricultural management and firm value: Evidence from Economics (Czech Republic), 60(7): 309 – 313. weather derivatives. The Journal of Finance, 68(5): VELECKÁ, M., JAVOROVÁ, J., FALTA, D. G. et al. 2143 – 2176. 2014. The Effect of Temperature and Time of Day PLATEN, E. and WEST, J. 2004. Fair pricing of weather on Welfare Indices in Loose – housed Holstein derivatives. [Online]. Available at: http://www.qfrc. Cows. Acta Universitatis Agriculturae et Silviculturae uts.edu.au/research/research_papers/rp106.pdf. Mendelianae Brunensis, 62(3): 565 – 570. [Accessed 2015, August 26]. ZAPRANIS, A. D. and ALEXANDRIDIS, ROUSTANT, O., LAURENT, J., BAY, X. and A. K. 2009. Weather Derivatives Pricing: CARRARO, L. 2003. Model risk in the pricing of weather Modeling the Seasonal Residual Variance of an derivatives. [Online]. Available at: http://laurent. Ornstein‑Uhlenbeck Temperature Process with jeanpaul.free.fr/weather_estimation_risk.pdf. Neural Networks. Neurocomputing, 73(1): 37 – 48. [Accessed 2015, August 26]. ZAPRANIS, A. D. and ALEXANDRIDIS, A. K. 2011. SCHILLER, F., SEIDLER, G. and WIMMER, M. Modeling and forecasting cumulative average 2012. Temperature models for pricing weather temperature and heating degree day indices for derivatives. Quantitative Finance, 12(3): 489 – 500. weather derivative pricing. Neural Computing and Applications, 20: 787 – 801.

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